1
MHT CET 2021 23th September Morning Shift
+2
-0

If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

A
$$\frac{2 h}{b-a}$$
B
$$\frac{2 h}{a-b}$$
C
$$\frac{h}{a+b}$$
D
$$\frac{2 h}{a+b}$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

A
$$\sqrt{3}\left(x^2+y^2\right)=2 x y$$
B
$$\sqrt{3}\left(x^2+y^2\right)=4 x y$$
C
$$4\left(x^2+y^2\right)=\sqrt{3} x y$$
D
$$2\left(x^2+y^2\right)=\sqrt{3} x y$$
3
MHT CET 2021 22th September Evening Shift
+2
-0

If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a =

A
$$-$$4
B
5
C
$$-$$2
D
$$-$$8
4
MHT CET 2021 22th September Evening Shift
+2
-0

If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockwise direction through an angle of $$15^{\circ}$$, then the equation of the line in new position is

A
$$y=3 x-6$$
B
$$y=\sqrt{3} x-2 \sqrt{3}$$
C
$$y=-\sqrt{3} x+2 \sqrt{3}$$
D
$$y=\frac{1}{\sqrt{3}} x-\frac{2}{\sqrt{3}}$$
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